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1500 questions
11
votes
6 answers
How can I convince students that Fourier series are useful?
Main question: Calculating the coefficients of a Fourier series can be difficult and time-consuming. How might a student be motivated/convinced to go through these (potentially tedious) details? Are there recognizable benefits that we, as teachers…
matqkks
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11
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An intuitive derivation of Taylor polynomial coefficients
I'd like to introduce Taylor polynomials by generalizing the linear approximation of a function $f(x)$ to a quadratic approximation.
The linear approximation formula $L(x)=f(a)+f'(a)(x-a)$ of $f(x)$ near $a$ can be seen to be the point-slope formula…
Jared
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11
votes
8 answers
What things should one know in order to enjoy their undergraduate degree?
From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is gruelling. However I'm certain that there are things that one could do to prepare in advance for the…
seeker
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11
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2 answers
Examples of proofs that use a cycle of implications to prove equivalence
I'm looking for some examples of proofs where it's easier to prove 'cyclical implications' $A\implies B\implies C\implies A$ than to prove $A\iff B$ directly.
I can think of some (relatively) advanced examples — but I'm looking for examples…
Grigory M
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11
votes
4 answers
How can I encourage my students to team work?
I have a motto, "My class is not an Olympic swimming pool! It is a museum full of the masterwork paintings! Relax and enjoy all of this mathematical beauty which I am drawing on the blackboard!"
By this sentence I mean that in my point of view the…
user230
11
votes
4 answers
Example for a theorem where the (more) formal proof is easier than other argumentation (e.g. imagination)
When students ask me for the use of the formal and abstract theory, I often would like to give answers they wouldn't understand. For instance, one application of abstract vector spaces and the banach fixed-point theorem is solving differential…
Anschewski
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11
votes
4 answers
How to overcome mathematics-related anxiety?
I'm in undergrad engineering, freshman year, in IT. I suffer anxiety when I have to do calculus. Trigonometry is just tortuous. Anyone got any tips for lessening that? I guess hard work is the best, but anything else? Anyone else had any personal…
Suraj Zala
11
votes
3 answers
Teaching how to read and translate word problems
High school students have a lot of trouble understanding word problems, and I don't know how to help them.
It's been too long since I've had trouble understanding usual word problems, so when I read the problem I automatically know what to do and…
Mark Fantini
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11
votes
4 answers
Topics that should be in an undergraduate math programme
According to your experience as students and professors, what are (and why) the courses that should be part of a math undergraduate degree, but that are missing in most institutions?
Dal
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11
votes
3 answers
Pedagogy, mathematics and Dieudonné's Foundations of Modern Analysis
I've heard from a friend of mine that Dieudonné's Foundations of Modern Analysis is "painful reading" and "a little outdated"; however, my teacher actually suggested it to me, describing it as a "wonderful text". So I would like to ask here if…
Dal
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11
votes
1 answer
What is the impact of such a device on math education?
Recently I found this device advertised which uses any mobile phone's built-in camera to solve equations.
From the site -
PhotoMath reads and solves mathematical expressions by using the
camera of your mobile device in real time. It makes math…
user 85795
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11
votes
3 answers
Teaching somebody else's class
How do you approach a class taught by somebody else?
There are multiple reasons why one could find him/herself in such a situation:
an instructor is sick,
there is a scheduled rotation of teachers,
you are visiting some other university and want…
dtldarek
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11
votes
2 answers
Test Correction Analysis
In hopes of helping my students practice and deepen their understanding of math knowledge, I wanted to bring up the topic of a test correction analysis - I didn't find much on this topic when I searched for it here.
So here's a screenshot of a test…
Gerardo
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11
votes
2 answers
The Use of Sound in Mathematics
I asked this question on Mathematics Stack Exchange first. It was well-received, but put on hold as off-topic. This site seems more appropriate. Here it is verbatim.
I'm not sure that this question is appropriate here. There's a good chance it's…
Shaun
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11
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3 answers
Regarding AMATYC's draft position statement on the academic preparation of mathematics faculty at two-year colleges
AMATYC has a draft position statement on the academic preparation of mathematics faculty at two-year colleges that will be voted on soon, if it hasn't happened already. The draft is attachment L in these minutes.
The draft states in part:
All…
alex.jordan
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